The bottom-of-the-table south coast club were placed in administration on Friday with debts of around 70 million pounds.
Portsmouth are now virtually certain to be relegated, with their 19-point tally being reduced next week when a nine-point deduction is activated after they became the first Premier League club to go into administration.
After they lose their points they will be 14 from the safety zone with 11 matches to play. However, on Saturday's evidence, if they are relegated they will not be going down without a fight.
Manager Avram Grant, who went to shake hands with the travelling fans after the game, told Sky Sports News: "Despite everything we were fighting today.
"You saw the spirit today, you see the real trait of people in difficult days. I still believe, I want to stay positive, that people will say 'wow.'
"Our target is to play positive football and I am very proud of the boys today and also in the last game.
"But football should be decided on the pitch, not by the actions of others. It is a game of passion for everyone from the Prime Minister to the elevator boy and it should be decided on what happens on the pitch," added Grant.
FINANCIAL PLIGHT
He said the players and the fans were being punished when other people were responsible for Portsmouth's financial plight.
"They are not punishing the right people," he said, "we did not do anything wrong."
Portsmouth took the lead through Frederic Piquionne after a fine flowing move in the 25th minute.
Martin Paterson equalised for Burnley with a lob over England keeper David James six minutes later but Portsmouth won thanks to a 76th-minute penalty from Hassan Yebda.
Earlier Jamie O'Hara saw his penalty saved by Burnley goalkeeper Brian Jensen while Portsmouth had Ricardo Rocha sent off in stoppage time.
Burnley, who made a good start to their first season back in the top flight for 33 years, have now won only one of their last 16 matches and are one place above Portsmouth on 23 points, a point behind Hull City.
The five teams above Hull are separated by three points and while Burnley's survival is not impossible, the home defeat to Portsmouth will do nothing for their confidence.
A despondent Burnley manager Brian Laws said: "We gifted them the three points. You should not lose at home against the bottom of the table team."
